In my experience, it depends on the specific funding of the program. Some programs funded by the NSF will require the applicants be Americans. But this is not always the case. Last year at my university, a student from Cambridge took part in the REU. 

When applying for funding for these programs, the directors must include some explanation of who will be the participants. Additionally, many of these programs specifically encourage minorities to apply, sometimes including non-American applicants.

I encourage you to look at the specific programs to see if they allow foreign applicants, emailing them if it is not stated on the webpage.

[Here][1] is the webpage that I used when searching for an REU as an undergrad.

Additionally, just googling "NSF REU 2010" is helpful.

  [1]: http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=5044